CODE 66204 2024/2025 5 cfu anno 1 INTERNET AND MULTIMEDIA ENGINEERING 10378 (LM-27) - GENOVA MAT/09 English GENOVA 2° Semester Questo insegnamento è un modulo di: AULAWEB

## OVERVIEW

Operations Research (OR) consists in a set of mathematical models and methods for solving decision problems in a very wide number of application sectors. The purpose of this course is to provide the students with competences in using a set of models for problem solving. In particular, the course mainly considers optimization problems faced by mathematical programming techniques and problems on graph and networks.

## AIMS AND CONTENT

### LEARNING OUTCOMES

This module aims to provide students with knowledge about a set of models and methods of Operations Research that will enable them to deal with decision problems. In particular, students will learn how to use mathematical linear programming models with continuous variables to formulate certain classes of decision problems, and they will learn how to find the optimal solution using the Simplex algorithm; in addition, students will learn how to perform sensitivity analysis and apply duality theory. A very important type of model that will be explained is the integer programming model that allows to face discrete decision problems; the branch and bound and cutting planes methods will be explained for this model. Finally, graph theory and network flow models will be presented; these classes of models are very important as they can model practical decision problems in telecommunications.

### AIMS AND LEARNING OUTCOMES

The main objective is to provide students with the skills to define mathematical programming models to solve a series of decision problems by formulating them as optimization problems. Students will be able to solve continuous and mixed integer programming problems using appropriate methods and algorithms. Students will be able to solve problems using networks flow models and graphs.The presented models and algorithms are fundamental tools for optimization in telecommunication.

### TEACHING METHODS

The course consists of classroom lectures.

### SYLLABUS/CONTENT

• Introduction to decisional problems and models. The process of problem formulation by means of quantitative models.
• Mathematical programming
• Basic definitions
• Linear programming.
• Graphic formulation and solution of linear programs.
• The simplex algorithm.
• Duality theory.
• Sensitivity analysis and economic interpretation.
• Integer programming and combinatorial optimization.
• Methods of cutting-planes and branch-and-bound.
• Graph and network theory.
• Shortest paths problems.
• Spanning tree problems..
• Max-flow and min cut problems. Network simplex algorithm.
• Introduction to TSP and routing problems.
• Basic concepts of the theory of complexity.
• Examples of heuristic algorithms for combinatorial problems
• Basic concepts of multi-criteria decision making

Frederick S Hillier, Gerald J Lieberman, Introduction to Operations Research, 9/e, McGraw-Hill Higher Education, 2010, ISBN: 0073376299

Students with learning disorders ("disturbi specifici di apprendimento", DSA) will be allowed to use specific modalities and supports that will be determined on a case-by-case basis in agreement with the delegate of the Engineering courses in the Committee for the Inclusion of Students with Disabilities.

## LESSONS

### LESSONS START

https://corsi.unige.it/10378/p/studenti-orario

### Class schedule

The timetable for this course is available here: Portale EasyAcademy

## EXAMS

### EXAM DESCRIPTION

Written exam text and oral exam (optional after passing the written text). The students who want to take the exam must register online and send an email to the professor.

### ASSESSMENT METHODS

The students will be asked to solve linear and integer programming problems using the learnt algorithms and applying concepts from theory. They have to be able to solve problems on graphs and networks. They have to demostrate to know the basic concepts of multi-criteria decision making.

Students with learning disorders ("disturbi specifici di apprendimento", DSA) will be allowed to use specific modalities and supports that will be determined on a case-by-case basis in agreement with the delegate of the Engineering courses in the Committee for the Inclusion of Students with Disabilities.

### FURTHER INFORMATION

Students who have a valid certification of physical or learning disabilities on file with the University and who wish to discuss possible accommodations or other circumstances regarding lectures, coursework, and exams should speak both with the instructor and with Professor Federico Scarpa (federico.scarpa@unige.it ), the School's disability liaison.